4 papers · 2 filters
Volume stability of plank covers
Egor Bakaev, Amir Yehudayoff
We prove a longstanding conjecture of András Bezdek on the stability of plank covers of the planar disk . If a sufficiently small disk is removed, then every fin…
Optimal partial plank coverings
Egor Bakaev, Alexander Polyanskii
A plank of width in a Euclidean space is the set of points lying between two parallel hyperplanes at distance from each other. Bang's theorem says that if a family of plank…
A simplex-based measure of symmetry
Egor Bakaev, Amir Yehudayoff
For compact convex sets , denote by the smallest size of a homothet of that contains . We define a measure of symmetry based on the -si…
A note on the affine plank conjecture
Egor Bakaev, Amir Yehudayoff
In 1951, Bang posed the affine plank conjecture, which remains open: If a convex body in is covered by planks, then the total relative width of the planks is at leas…